For a two-dimensional problem we could write (27) in terms of a stream function for the flow velocity \(\mathbf {v}\) . If we omit the quantum potential term and set \(\varepsilon =0\)  in (27) we obtain a time symmetric equation which admits solutions in both time directions. In contrast, the Schrödinger equation admits solutions only in one direction in time and its complex conjugate in the opposite one. In that limit (27) is reduced to an inhomogeneous wave equation with a Lighthill source term [1]}, [2]} and its solution is
\(\rho (\mathbf {x},t) = \frac{1}{4\pi c_{0} ^{2}}\frac{\partial ^{2}}{\partial x_{i}\partial x_{j}}\int _{-\infty }^{+\infty } \frac{T_{ij}\left(\mathbf {y},t-\frac{|\mathbf {x}-\mathbf {y}|}{c_{0}}\right)+ T_{ij}\left(\mathbf {y},t+\frac{|\mathbf {x}-\mathbf {y}|}{c_{0}}\right)}{|\mathbf {x}-\mathbf {y}|}d^{3}\mathbf {y},\) 
